QLM demodulation

ABSTRACT

A method for deriving a bound on communications capacity with ideal quadrature layered communications QLM and a set of demodulation algorithms for QLM. Communications links using QLM can approximate this bound and support higher data rates than allowed by the Shannon bound. Demodulation algorithms can be grouped into symbol algorithms and bit algorithms. Bit algorithms support higher data rates than symbol algorithms with lower computational complexities at the expense of demodulation loss which can be reduced with bit correlation error correction decoding which is orthogonal to the channel error correction decoding. Representative symbol and bit implementation algorithms are derived. Modulation performance is compared with phase-shift-keying PSK and quadrature amplitude modulation QAM. The invention describes how QLM can be used with PSK, QAM and with gaussian minimum shift keying GMSK, orthogonal frequency division multiple access OFDMA, code division multiple access CDMA, and wavelet division multiple access WDMA.

CROSS-REFERENCE TO RELATED APPLICATIONS

This patent application is a continuation in part of application Ser.Nos. 10/826,118 filed on Apr. 16, 2004, now U.S. Pat. No. 7,006,830,10/266,256 filed on Oct. 8, 2002, now U.S. Pat. No. 7,391,819 andapplication Ser. No. 10/772,597 filed on Feb. 6, 2004 now U.S. Pat. No.7,337,383.

U.S. PATENT DOCUMENTS

U.S.-9.826,117 October 2007 von der Embse, U. A. U.S. Pat. No. 7,010,048March 2006 Shattil, Stephen J. U.S.-6-856,652 February 2006 West et. al.U.S.-2002/0176486 November 2002 Okubo, et. al. U.S.-2002/0101936 August2002 Wright et. al. U.S.-2002/0031189 March 2002 Hiben et. al. U.S. Pat.No. 6,804,307 October 2004 Popović, Branislav SE U.S. Pat. No. 6,798,737September 2004 Dabak et. al. U.S. Pat. No. 6,731,618 May 2004 Chung et.al. U.S. Pat. No. 6,731,668 May 2004 John Ketchum U.S. Pat. No.6,728,517 April 2004 Sugar et. al. U.S. Pat. No. 6,711,528 March 2004Dishman et. al. U.S. Pat. No. 6,687,492 February 2004 Sugar et. al. U.S.Pat. No. 6,674,712 January 2004 Yang et. al. U.S. Pat. No. 6,647,078November 2003 Thomas et. al. U.S. Pat. No. 6,636,568 October 2003 TamerKadous U.S. Pat. No. 6,504,506 January 2003 Thomas et. al. U.S. Pat. No.6,426,723 July 2003 Smith et. al.

U.S. PATENT APPLICATIONS

U.S. application Ser. No. 10/772,597 February 2004 von der Embse, U. A.U.S. application Ser. No. 10/266,256 October 2002 von der Embse, U. A.U.S. application Ser. No. 09/846,410 February 2001 von der Embse, U. A.U.S. application Ser. No. 09/826,118 January 2001 von der Embse, U. A.

OTHER PUBLICATIONS

-   C. Heegard and S. B. Wicker's book “Turbo Coding”, Kluwer Academic    Publishers 1999-   B. Vucetic and J. Yuan's book “Turbo Codes”, Kluwer Academic    Publishers 2000-   J. G. Proakis's book “Digital Communications”. McGraw Hill, Inc.    1995-   L. Hanzo, C. H. Wong, M. S. Lee's book “Adaptive Wireless    Transceivers”, John Wiley & Sons 2002-   C. E. Shannon “A Mathematical Theory of Communications”, Bell System    Technical Journal, 27:379-423, 623-656, October 1948

BACKGROUND OF THE INVENTION

I. Field of the Invention

The present invention relates to the Shannon bound on communicationscapacity and also relates to symbol modulation and demodulation forhigh-data-rate wired, wireless, and optical communications and includesthe symbol modulations phase-shift-keying PSK, quadrature amplitudemodulation QAM, bandwidth efficient modulation BEM, gaussian minimumshift keying GMSK, pulse position modulation PPM, and the plurality ofcurrent and future modulations for single links and multiple accesslinks which include time division multiple access TDMA, frequencydivision multiple access FDMA, code division multiple access CDMA,spatial division multiple access SDMA, frequency hopping FH, opticalwavelength division multiple access WDMA, orthogonal Wavelet divisionmultiple access OWDMA, combinations thereof, and the plurality of radar,optical, laser, spatial, temporal, sound, imaging, and mediaapplications. Communication application examples include electrical andoptical wired, mobile, point-to-point, point-to-multipoint,multipoint-to-multipoint, cellular, multiple-input multiple-output MIMO,and satellite communication networks.

II. Description of the Related Art

The Shannon bound is the Shannon capacity theorem for the maximum datarate C and equivalently can be restated as a bound on the correspondingnumber of modulation bits per symbol as well as a bound on thecommunications efficiency and is complemented by the Shannon codingtheorem. From Shannon's paper “A Mathematical Theory of Communications”Bell System Technical Journal, 27:379-423, 623-656, October 1948 and B.Vucetic and J. Yuan's book “Turbo Codes”, Kluwer Academic Publishers2000, the Shannon (Shannon-Hartley theorem) capacity theorem, thecorresponding Shannon bound on the information bits b per symbol, theShannon bound on the communications efficiency η, and the Shannon codingtheorem can be written as equations (1).

$\begin{matrix}{{{{{Shannon}\mspace{14mu}{bounds}\mspace{14mu}{and}\mspace{14mu}{coding}\mspace{14mu}{theorem}}\mspace{14mu}{1.\mspace{14mu}{Shannon}\mspace{14mu}{capacity}\mspace{14mu}{theorem}}\mspace{20mu}\begin{matrix}{C = {B\mspace{11mu}{\log_{2}\left( {1 + {S/N}} \right)}}} \\{{= {{{Channel}\mspace{14mu}{capacity}\mspace{14mu}{in}\mspace{14mu}{bits}\text{/}{second}} = {{Bps}\mspace{14mu}{for}\mspace{14mu}{an}}}}\mspace{14mu}} \\{{additive}\mspace{14mu}{white}\mspace{14mu}{Gaussian}\mspace{14mu}{noise}\mspace{14mu} A\; W\; G\; N\mspace{14mu}{channel}} \\{{{with}\mspace{14mu}{bandwidth}\mspace{14mu} B\mspace{14mu}{wherein}\mspace{14mu}{``\log_{2}"}\mspace{14mu}{is}\mspace{14mu}{the}}\mspace{14mu}} \\{{logarithm}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{base}\mspace{14mu} 2} \\{= {{Maximum}\mspace{14mu}{rate}\mspace{14mu}{at}\mspace{14mu}{which}\mspace{14mu}{information}\mspace{14mu}{can}\mspace{14mu}{be}}} \\{{{reliably}\mspace{14mu}{transmitted}\mspace{14mu}{over}\mspace{14mu} a\mspace{14mu}{noisy}\mspace{14mu}{channel}}\mspace{14mu}} \\{{where}\mspace{14mu}{S/N}\mspace{14mu}{is}\mspace{14mu}{the}\mspace{11mu}\text{signal-to-noise}\mspace{14mu}{ratio}\mspace{14mu}{in}\mspace{14mu} B}\end{matrix}}{{2.\mspace{14mu}{Shannon}\mspace{14mu}{bound}\mspace{14mu}{on}\mspace{14mu} b},\eta,{{and}\mspace{14mu}{E_{b}/N_{o}}}}\begin{matrix}{\mspace{31mu}{{\max\left\{ b \right\}} = {\max\left\{ {C/B} \right)}}} \\{= {\log_{2}\left( {1 + {S/N}} \right)}} \\{= {\max(\eta)}} \\{{E_{b}/N_{o}} = {{\left\lbrack {{{2\hat{}\max}\left\{ b \right\}} - 1} \right\rbrack/\max}\left\{ b \right\}}}\end{matrix}\mspace{34mu}{wherein}}\mspace{34mu}{{b = {C/B}},\mspace{14mu}{{{Bps}\text{/}{Hz}} = {{Bits}\text{/}{symbol}}}}\mspace{34mu}{{\eta = {{b/T_{s}}B}},\mspace{14mu}{{Bps}\text{/}{Hz}}}\mspace{34mu}{T_{s} = {{symbol}\mspace{14mu}{interval}}}{3.\mspace{14mu}{Shannon}\mspace{14mu}{coding}\mspace{14mu}{theorem}\mspace{14mu}{for}\mspace{14mu}{the}\mspace{14mu}{infomation}\mspace{14mu}{bit}}\mspace{31mu}{{rate}\mspace{14mu} R_{b}}\begin{matrix}{\mspace{31mu}{{{For}\mspace{14mu} R_{b}} < C}} & {{{there}\mspace{14mu}{exists}\mspace{14mu}{codes}\mspace{14mu}{which}\mspace{14mu}{support}}\mspace{14mu}} \\\; & {{reliable}\mspace{14mu}{communications}} \\{\mspace{31mu}{{{For}\mspace{14mu} R_{b}} > C}} & {{{there}\mspace{14mu}{are}\mspace{14mu}{no}\mspace{14mu}{codes}\mspace{14mu}{which}\mspace{14mu}{support}}\mspace{14mu}} \\\; & {{reliable}\mspace{14mu}{communications}}\end{matrix}} & (1)\end{matrix}$

Using the assumption that the symbol rate 1/T_(s) is maximized whichmeans 1/T_(s)=Nyquist rate=bandwidth B and is equivalent T_(s)B=1,enables 1 in equations (1) defining C to be rewritten to calculatemax{b} as a function of the signal-to-noise ratio S/N, and to calculateE_(b)/N_(o) which is the ratio of energy per information bit E_(b) tothe noise power density N_(o), as a function of the max{b} in 2 andwherein max{b} is the maximum value of the number of information bitsper symbol b. Since the communications efficiency η=b/(T_(s)B) inbits/sec/Hz it follows that maximum values of b and η are equal. Thederivation of the equation for E_(b)/N_(o) uses the definitionE_(b)/N_(o)=(S/N)/b in addition to 1 and 2. Reliable communications inthe statement of the Shannon coding theorem 3 means an arbitrarily lowbit error rate BER.

SUMMARY OF THE INVENTION

This invention introduces a bound on communications capacity that can besupported by a communications channel with frequency bandwidth B andsignal-to-noise ratio S/N, a quadrature parallel-layered modulation QLM,and QLM demodulation algorithms. QLM is used to derive this bound andthe QLM performance validates the bound by providing a modulation whichbecomes close to this bound with error correcting codes such as turbocodes. QLM is a layered topology for transmitting higher data rates thanpossible with each layer of communications and is implemented bytransmitting each layer with a differentiating or equivalently adiscriminating parameter which enables separation and decoding of eachlayer. Performance verification of a representative trellis demodulationalgorithm is given for QLM modulation using PSK for each layer. Symboldemodulation algorithms primarily are maximum likelihood ML and trellisalgorithms. Trellis algorithms provide the best demodulation performanceat the cost of computational complexity. Suboptimal reduced-stateiterative trellis demodulation algorithms help to reduce thecomputational complexity. A second category of demodulation algorithmsare trellis bit algorithms which offer substantially lower complexitydemodulation at the cost of a demodulation loss. This loss can bereduced with bit correlation error correction decoding which coding isorthogonal to the normal bit sequential error correction decoding ofeach communication channel.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

The above-mentioned and other features, objects, design algorithms, andperformance advantages of the present invention will become moreapparent from the detailed description set forth below when taken inconjunction with the drawings and performance data wherein likereference characters and numerals denote like elements, and in which:

FIG. 1 calculates information bits b per symbol interval versusE_(b)/N_(o) for the new bound, Shannon bound, and for PSK, QAM atBER=1e−6 with turbo coding.

FIG. 2 calculates information bits b per symbol interval versus S/N=C/Ifor the new bound, Shannon bound, and for PSK, QAM at BER=1e−6 withturbo coding wherein C/I is the carrier power to interference powerratio in B.

FIG. 3 calculates the performance of QLM PSK and QLM QAM asBps/Hz=Bits/(symbol Interval)=b vs. E_(b)/N_(o).

FIG. 4 calculates the performance of QLM PSK and QLM QAM asBps/Hz=Bits/(symbol Interval)=b vs. S/N=C/I.

FIG. 5 plots the ideal waveform in time and frequency, the correlationfunction of the waveform, and a QLM correlation function for n_(p)=4.

FIG. 6 plots a OWDMA Wavelet waveform in time, the Wavelet correlationfunction in time, and the ideal correlation function in time.

FIG. 7 plots a OFDMA DFT waveform in frequency, the DFT correlationfunction in frequency, and the ideal correlation function in frequencywherein DFT is the discrete fourier transform.

FIG. 8 illustrates the pulse waveform time offsets for QLM with n_(p)layers of communications.

FIG. 9A is a block diagram of a trellis symbol demodulation algorithm.

FIG. 9B is the flow diagram of the trellis symbol demodulationalgorithm.

FIG. 9C is the continuation of the flow diagram of the trellis symboldemodulation algorithm.

FIG. 10 plots the measured bit error rate BER performance for theuncoded 4-PSK QLM with a n_(p)=2 layered QLM pulse waveform in FIG. 8using the trellis demodulation algorithm in FIG. 9.

FIG. 11 is a block diagram of a QLM trellis symbol iterativedemodulation algorithm.

FIG. 12 plots complexity metric performance of a trellis symboldemodulation algorithm vs. the information bits b.

FIG. 13 plots complexity metric performance of a trellis bitdemodulation algorithm vs. the information bits b.

FIG. 14 illustrates decisioning manifolds for 8-PSK for the first twobits of the 3 bit 8-PSK data symbol.

FIG. 15 is a block diagram of a QLM trellis bit demodulation algorithm.

FIG. 16 is a block diagram of a QLM trellis bit iterative demodulationalgorithm.

FIG. 17 is a representative transmitter implementation block diagram forOFDMA QLM.

FIG. 18 is a representative transmitter implementation block diagram forCDMA QLM.

FIG. 19 is a representative transmitter implementation block diagram forOWDMA QLM.

FIG. 20 is a representative receiver implementation block diagram forOFDMA QLM.

FIG. 21 is a representative receiver implementation block diagram forCDMA QLM.

FIG. 22 is a representative receiver implementation block diagram forOWDMA QLM.

DETAILED DESCRIPTION OF THE INVENTION

Quadrature parallel-layered modulation QLM is a new invention thatincreases the data rate supported by a channel by adding layers ofindependent communications channels or signals over the existingcommunications such that each layer can be uniquely separated anddemodulated in the receiver. These layers of communications channels areparallel sets of communications channels occupying the same bandwidth Bas the 1^(st) layer which is the original set of communications channelsoccupying the bandwidth B. Layering of parallel channels or signals isnot necessarily an addition of signals in the algebra of the real orcomplex field since for example for GMSK the layering is in thefrequency domain of the FM signal.

The new bound on communications capacity recognizes that one canincrease the average symbol rate from the Nyquist rate 1/T_(s)=B assumedin the Shannon bound in equations (1) to the valuen_(p)/T_(s)=n_(p)B=n_(p)x(Nyquist Rate) with n_(p) layers of thecommunications or equivalently with the addition of (n_(p)−1) parallelcommunications channels with differing characteristics which make themseparable and recoverable in the receiver with implementation of atrellis type demodulation algorithm or the equivalent in terms ofcapabilities and performance where “equivalent” includes the pluralityof all possible mathematical techniques to provide alternative solutionscompared to the broad class of trellis algorithms. Note that “×” is themultiplication symbol for “times”. In this patent disclosure the term“separable” is intended to mean there is a differentiating parameter orequivalently a discriminating parameter which allows the n_(p) layers orequivalently channels to be uniquely recoverable.

The capacity bound and coding theorem in equations (5) are derived forconvenience using time as the differentiating parameter withoutrestrictions on the differentiating parameter. Step 1 in the derivationobserves a suitably constructed trellis algorithm will successfullyinvert the transmitted layers 1, . . . , n_(p) of communicationschannels for QLM to recover estimates of the transmitted symbols whenthe layers are time synchronized for transmission atT_(s)/n_(p)2T_(s)/n_(p), . . . , (n_(p)−1)T_(s)/n_(p) offsetsrespectively for layers 2,3, . . . , (n_(p)−1) relative to the 1^(st)layer at zero offset corresponding to transmitting symbols at ΔT_(s)intervals with ΔT_(s)=T_(s)/n_(p). Maximum capacity for each layer isequal to the Shannon bound in 1 in equations (2) which is the Shannonbound in 2 in equations (1) with b, S/N replaced by b_(p), (S/N)_(p) foreach layer with the subscript “p” referring to each communicationslayer. Maximum capacity b in 2 in equations (2) for the n_(p) layers isthe product of n_(p) and b_(p)

Step 11 max{b _(p)}=log₂[1+(S/N)_(p)]2. b=n _(p) log₂[1+(S/N)_(p)]  (2)where b=n_(p)b_(p)=Bps/Hz=Bits/(Symbol Interval) is the number of bitsover a T_(s) interval, (S/N)_(p)=S/N per symbol in each of theparallel-layered communications sets of channels, and the maximum labelfor b has been removed since there is a dependency on both n_(p) and(S/N)_(p) which must be defined in order to transform this equation intoa maximum for b.

Step 2 observes the communications layers will equally share in thetransmitted S/N and the signal power available for demodulation in eachlayer is equal to the signal power in each layer over the separationinterval ΔT_(s). This means for demodulation, each layer receives thesignal power over the fraction ΔT_(s)=T_(s)/n_(p) of the symbol intervalT_(s) and n_(p)(S/N)_(p)=(S/N)_(s) is equal to the signal to noise ratio(S/N)_(s) over T_(s) for each layer in 1 in equations (3). The total S/Nover T_(s) is the sum of the (S/N)_(s) for each layer which yields 2 inequations (3).

Step 21 n _(p)(S/N)_(p)=(S/N)_(s)2 S/N=(n _(p)^2)(S/N)_(p)  (3)

Results of steps 1 and 2 are used to derive the E_(b)/N_(o) from thevalue (E_(b)/N_(o))_(p) in each layer. Substituting the identitiesS/N=bE_(b)/N_(o), (S/N)_(p)=b_(p)(E_(b)/N_(o))_(p), and b=n_(p)b_(p)into 2 in equations (3) yields equation (4).E _(b) /N _(o) =n _(p) (E _(b) /N _(o))_(p)  (4)

Equations (2) and (3) for step 1 and step 2 respectively can be combinedwith the identity S/N=bE_(b)/N_(o) to yield the equations (5) for thenew bounds on C, max{b}, and max{η} as a function of S/N, E_(b)/N_(o)and for the minimum E_(b)/N_(o) written as min{E_(b)/N₀} as a functionof b wherein the optimization is over the number of communicationslayers n_(p).

Upper bounds for b and η defined in 2 in equations (5) are derived from2 in equations (2), 2 in equations (3), and the identitiesS/N=bE_(b)/N_(o) and max(η}=max{b} in the form of a maximum with respectto the selection of the parameter n_(p) for fixed values of S/N in thefirst expression and in the second for fixed values of E_(b)/N_(o) withan interactive evaluation of b from the first expression.

Upper bound for C in 1 in equations (5) is derived from the capacityequation for max{b} in 2 in equations (2) and the identities b=C/B andS/N=bE_(b)/N_(o) in the form of an upper bound on C with respect to theselection of the parameter n_(p) for fixed values of S/N in the firstexpression and in the second for fixed values of E_(b)/N_(o) with aninteractive evaluation of b from 2.

Lower bound on E_(b)/N_(o) which is the minimum value min{E_(b)/N_(o)}in 3 in equations (5) is derived by solving the second expression in 2and taking the minimum over all allowable values of n_(p).

The new coding theorem in 4 in equations (5) states that C is the upperbound on the information data rate R_(b) in bits/second for which errorcorrecting codes exist to provide reliable communications with anarbitrarily low bit error rate BER where C is defined in 1 in equations(5) and upgrades the Shannon coding theorem 3 in equatios (1) using newcapacity bound C in 1 in equations (5) and introduces the new datasymbol rate 5 whose maximum value max{n_(p)/T_(s)} is n_(p) times theNyquist rate for a bandwidth B.

$\begin{matrix}{\left. {{{New}\mspace{14mu}{capacity}\mspace{14mu}{bounds}\mspace{14mu}{and}\mspace{14mu}{coding}\mspace{14mu}{theorem}}{1.\mspace{11mu}\begin{matrix}{C = {\max\left\{ {n_{p}B\;{\log_{2}\left\lbrack {1 + {\left( {S/N} \right)/{n_{p}\hat{}2}}} \right\rbrack}} \right\}}} \\{= {\max\left\{ {n_{p}B\;{\log_{2}\left\lbrack {1 + {\left( {{bE}_{b}/N_{o}} \right)/{n_{p}\hat{}2}}} \right\rbrack}} \right\}}}\end{matrix}}{2.\;\begin{matrix}{\;{{\max\left\{ b \right\}} = {\max\left\{ {n_{p}{\log_{2}\left\lbrack {1 + {\left( {S/N} \right)/{n_{p}\hat{}2}}} \right\rbrack}} \right\}}}} \\{= {\max\left\{ {n_{p}{\log_{2}\left\lbrack {1 + {\left( {{bE}_{b}/N_{o}} \right)/{n_{p}\hat{}2}}} \right\rbrack}} \right\}}} \\{= {\max\left\{ \eta \right\}}}\end{matrix}}{{3.\mspace{14mu}\min\left\{ {E_{b}/N_{o}} \right\}} = {\min\left\{ {{{\left\lbrack {{n_{p}\hat{}2}/b} \right\rbrack\left\lbrack {2\hat{}b} \right\}}/n_{p}} - 1} \right\rbrack}}} \right\}{4.\mspace{14mu}{New}\mspace{14mu}{coding}\mspace{14mu}{theorem}}\mspace{31mu}\begin{matrix}{{{For}\mspace{14mu} R_{b}} < C} & {{{there}\mspace{14mu}{exists}\mspace{14mu}{codes}\mspace{14mu}{which}\mspace{14mu}{support}}\mspace{14mu}} \\\; & {{reliable}\mspace{14mu}{communications}} \\{{{For}\mspace{14mu} R_{b}} > C} & {{{there}\mspace{14mu}{are}\mspace{14mu}{no}\mspace{14mu}{codes}\mspace{14mu}{which}\mspace{14mu}{support}}\mspace{14mu}} \\\; & {{reliable}\mspace{14mu}{communications}}\end{matrix}{5.\mspace{14mu}{New}\mspace{14mu}{symbol}\mspace{14mu}{rate}\mspace{14mu}{n_{p}/T_{s}}}\begin{matrix}{\mspace{31mu}{{\max\left\{ {n_{p}/T_{s}} \right\}} = {n_{p}B\mspace{14mu}{for}{\mspace{11mu}\;}n_{p}\mspace{14mu}{layers}\mspace{14mu}{of}\mspace{14mu}{communications}}}} \\{= {n_{p}x\mspace{14mu}\left( {{Nyquist}\mspace{14mu}{rate}} \right)}}\end{matrix}} & (5)\end{matrix}$

FIG. 1,2 calculate the Shannon bound 63,68, the new bound 62,67, thequadrature amplitude QAM and phase shift keying PSK turbo codedperformance, and the QLM performance example from equations (6). The newbound is from equations (4),(5) and the Shannon bound from equations (1)wherein the units for b are Bps/Hz=bits/(symbol interval) consistentwith the Shannon bound where “symbol interval” refers to the T_(s)interval The turbo coded PSK 65,70 and turbo coded QAM 66,71 plot thenumber of information bits per symbol b versus measured S/N andE_(b)/N_(o) for 4-PSK, 8-PSK, 16-QAM, 64-QAM, 256-QAM, 4096-QAM. The4-PSK, 8-PSK are 4-phase, 8-phase phase shift keying modulations whichrespectively encode 2,3 bits per symbol and 16-QAM, 64-QAM, 256-QAM,1024-QAM are 16,64, 256, 4096 state QAM modulations which respectivelyencode 4,6,8,12 bits. For no coding the information bits per symbol b isequal to the modulation bits per symbol b_(s) so thatb=b_(s)=2,3,4,6,8,12 bits per symbol respectively for 4-PSK, 8-PSK,16-QAM, 64-QAM, 256-QAM, 4096-QAM. Turbo coding performance assumes amodest 4 state recursive systematic convolutional code RSC, 1024 bitinterleaver, and 4 turbo decoding iterations. The assumed coding ratesR=3/4, 2/3, 3/4, 2/3, 3/4, 2/3 reduce the information bits per symbol tothe respective values b=1.5,2,3,4,6,8 bits. Performance data is from C.Heegard and S. B. Wicker's book “Turbo Coding”, Kluwer AcademicPublishers 1999, B. Vucetic and J. Yuan's book “Turbo Codes”, KluwerAcademic Publishers 2000, J. G. Proakis's book “Digital Communications”,McGraw Hill, Inc. 1995, and L. Hanzo, C. H. Wong, M. S. Lee's book“Adaptive Wireless Transceivers”, John Wiley & Sons 2002.

FIG. 1,2 calculate the coded QLM performance 64,69 using equations (6)for QLM PSK (which reads “QLM modulation using PSK data symbolmodulation”) using the scaling laws for E_(b)/N_(o)=n_(p)(E_(b)/N_(o))_(p) in equations (4) and for S/N=(n_(p)^2) (S/N)_(p) in 2in equations (3). In 1 examples of QLM PSK for 4,8-PSK are given forb=3,4,6,8,12,16 bits per symbol interval as functions of b_(s)=2,3uncoded bits per data symbol for 4,8-PSK, QLM layers n_(p)=2,4,8, andcoding rate R=(information bits/data bits)=2/3,3/4. It is well knownthat the most bandwidth efficient coding for 4,8-PSK use R=3/4,2/3 in 1.In 2 the corresponding values of E_(b)/N_(o)=3.0,4.1 dB for 4,8-PSK atBER=1e−6 are from the turbo coding data in FIG. 1, 2. In 3 theE_(b)/N_(o) for n_(p) layers is calculated from the measured values forthe 1^(st) or ground layer in 2 using equations (3). In 4 the S/N iscalculated as a function of the E_(b)/N_(o) in 3,4 and the b in 1. Itshould be clear that the combinations of parameters b_(s),n_(p),R in 1in equations (6) are a limited subset of possible values. The selectedsubset is intended to illustrate the principles, algorithms,implementation, and performance, and is not necessarily the preferredsubset for overall performance.

QLM PSK performance (6) 1 Information bits b per symbol $\begin{matrix}{P\; S\; K} & {b_{s} \times n_{p} \times R} & = & b \\\text{4-PSK} & {2 \times 2 \times {3/4}} & = & 3 \\\text{8-PSK} & {3 \times 2 \times {2/3}} & = & 4 \\\text{4-PSK} & {2 \times 4 \times {3/4}} & = & 6 \\\text{8-PSK} & {3 \times 4 \times {2/3}} & = & 8 \\\text{4-PSK} & {2 \times 8 \times {3/4}} & = & 12 \\\text{8-PSK} & {3 \times 8 \times {2/3}} & = & 16\end{matrix}$

-   2 PSK turbo coding measurements    -   4-PSK E_(b)/N_(o)=3.0 dB        -   for turbo coding, rate R=3/4, BER=1e−6    -   8-PSK E_(b)/N_(o)=4.1 dB        -   for turbo coding, rate R=2/3, BER=1e−6-   3 E_(b)/N_(o) estimates    -   4-PSK E_(b)/N_(o)=3.0+10 log₁₀(n_(p)) dB    -   8-PSK E_(b)/N_(o)=4.1+10 log₁₀(n_(p)) dB-   4 S/N estimates    -   S/N=E_(b)/N_(o)+10 log₁₀(b), dB

FIG. 3,4 calculate some of the available options for supportingb=Bps/Hz=bits/(symbol interval) performance to 12 Bps/Hz using thescaling laws for E_(b)/N_(o)=n_(p) (E_(b)/N_(o))_(p) in equations (4),the scaling laws for S/N=(n_(p)^2)(S/N)_(p) in equations (3), the QLMbound, and the 4-PSK, 8-PSk, 16-QAM, 64-QAM, 256-QAM modulations. FIG. 3calculates the QLM bound in 24, the QLM 4-PSK b vs. E_(b)/N_(o) in 25for n_(p)=1,2,4,8, the QLM 8-PSK b vs. E_(b)/N_(o) in 26 forn_(p)=1,2,4,6 in 26, and the QLM 16-QAM, 64-QAM, 256-QAM b vs.E_(b)/N_(o) for n_(p)=1,2,4, n_(p)=1,2,3, n_(p)=1,2, respectively in 27,28, 29. FIG. 4 calculates the QLM bound in 30 and these modulations forb vs. S/N=C/I for 4-PSK in 31, 8-PSK in 32, 16-QAM in 33, 64-QAM in 34,and 256-QAM I 35. To achieve b=12 Bps/Hz=Bits/(symbol length) the QLM4-PSK, 8-PSK, 16-QAM, 64-QAM, 256-QAM require successively fewer layersof communications n_(p)=8,6,4,3,2 with attendant successively highervalues for the required E_(b)/N_(o) and S/N=C/I.

Demodulation algorithms for QLM implement the steps in the signalprocessing (7):

QLM Demodulation Signal Processing (7)

-   -   step 1 detects the received QLM signal to remove the waveform        and recover the stream of correlated transmitted data symbols at        the rate n_(p)/T_(s)=n_(p)B data symbols per second,    -   step 2 processes this stream of correlated data symbols to        recover estimates of the data symbols for each of the n_(p)        communication channels or sets of channels or layers, and    -   step 3 converts the data symbol stream for each channel or each        set of channels to a data bit stream and implements error        correction decoding of the data bit stream to recover estimates        of the transmitted data bits.

In step 2 the ability of the demodulation algorithms to recover thetransmitted data symbols from the received QLM communications signaldepends on the correlation (auto-correlation) function beingwell-behaved. A correlation function of a discriminating parameter orequivalently a differentiating parameter such as time offset orfrequency offset enables the QLM layers to be demodulated to recover thetransmitted data symbols. Plots of representative correlation functionsin time and frequency offsets are given in FIG. 5,6,7. The correlationsin FIG. 5,6,7 are used to implement step 2 of the demodulation signalprocessing (7) since their symmetry property makes these correlationsequal to convolutions of the waveforms with their stored replicas whichis a requirement in step 2 of the demodulation signal processing (7).

FIG. 5 presents an ideal impulse response waveform (pulse waveform) inboth time and frequency and the corresponding correlation in time andfrequency. In time 12 the ideal impulse response 10 waveform 11 extendsover the data symbol T_(s) second interval 13 and has a correlationfunction 14 in time 15 with a triangular mainlobe 16 extending over2T_(s) seconds 18 with zero sidelobes 17. This waveform is the idealpulse waveform in FIG. 8. In frequency 12 the ideal impulse response 10waveform 11 extends over the frequency interval B Hz 13 and has acorrelation function 14 in frequency 15 with a triangular mainlobe 16extending over 2B Hz 18 with zero sidelobes 17. The correlation functionfor the pulse waveform in FIG. 8 for n_(p)=4 is overlayed on thetriangular correlation function as a set of circles 19 on the mainlobeand on the sidelobes 17. It is observed there are 2n_(p)−1=2×4−1=7correlation values in the mainlobe.

FIG. 6 presents a Wavelet waveform in patent application 09/826,118 forOWDMA in time, the correlation function, and an ideal correlationfunction in time. The correlation function closely approximates thewaveform and the ideal triangular correlation closely approximates themainlobe and has a mainlobe 20 extending over 2T_(s) second intervalwith low sidelobes 21.

FIG. 7 presents a N=64 point discrete fourier transform DFT for OFDMA infrequency, the correlation function, and an ideal correlation functionin frequency. The correlation function closely approximates the waveformand the ideal triangular correlation closely approximates the mainlobeand has a mainlobe extending over 2B=2/T_(s) Hz interval with lowsidelobes 23 wherein the symbol rate 1/T_(s) is at the Nyquist rate andequal to the bandwidth B for each channel.

FIG. 8 defines the QLM modulation for an ideal pulse modulation withtiming offset as the differentiating parameter between the QLM layersand whose waveform and correlation function are defined in FIG. 5. Thereference pulse 33 p_(i)=p_(i)(t) defined over time 34 t is 35 T_(s)seconds long and normalized with amplitude 36 1/T_(s). Starting time 37is t=i₁T_(s) and ending time 38 is T_(s) seconds later. Indexingconvention is a pulse i has no offset relative to the reference time,pulse i+1 41 has a ΔA_(s) offset 37, pulse i−1 43 has a −ΔT_(s) offset37, and this convention applies to all i. Symbol modulation 39Ae^(jΦ_(i)) when multiplied by the pulse amplitude 36 1/√{square rootover (T_(s))} is the complex envelope of the pulse waveform. Consecutivepulses are spaced at 40 ΔT_(s)=T_(s)/n_(p) second intervals. Also shownare the consecutive later pulse 41 and the continuation 42, and theearlier pulses 43 and 44 and the continuation 45. Starting times forthese additional pulses are given in 37. This QLM architecture has apulse overlap of nearest neighbor pulses with a correspondingcorrelation between these pulses given in FIG. 5 for n_(p)=4 pulses orlayers.

Step 2 demodulation algorithms are grouped into maximum likelihood MLsymbol algorithms, trellis symbol algorithms, and trellis bitalgorithms. Trellis symbol algorithms are trellis algorithms over thecorrelated data symbol fields and use ML, maximum a-posteriori MAP, orother decisioning metrics. Trellis bit algorithms are trellis algorithmsover the data symbol correlated bit fields. MAP decisioning metrics havebeen introduced in patent application Ser. No. 10/772,597 for trellisand convolutional decoding using trellis algorithms. This classificationof demodulation algorithms is introduced to illustrate representativemethods for constructing demodulation algorithms and is not a limitationon the scope of this invention which encompasses all possibledemodulation algorithms for QLM.

For step 2 consider a ML symbol detection algorithm using a blockalgorithm approach with the pulse waveform in FIG. 8. Demodulation forQLM implements signal detection in step 1 to remove the waveform andrecover estimates of the transmitted complex baseband signal in step 2followed by signal decoding in step 3 to recover estimates of thetransmitted data. The received pulse waveform is removed by aconvolution of the received signal {circumflex over (z)}(t) with thecomplex conjugate of the transmitted pulse waveform and this receiverconvolution generates the received Rx estimate Y_(i)=X_(i)+n_(i) of thetransmitted Tx symbol wherein the received noise-free waveform aftersymbol detection is X_(i)=Σ_(δi) Z_(i+δi) c(δi) equal to the correlatedsum of the data symbols Z_(i+δi)=A_(i+δi) e^(jφ_(i+δi)) with each datasymbol encoded with the signal amplitude A_(i) and signal phase φ_(i)for PSK and QAM symbol encoding and where c(δi) is the correlationcoefficient of the pulse waveform p_(i)(t) in FIG. 5,8 over neighboringsymbols at i+δi=i+/−1,i+/−2, . . . in FIG. 8 and by definitionc(δi)=∫p_(i)(t)p_(i+δi)(t)dt which is normalized so that c(0)=1, andn_(i) is the data symbol detection noise. Also, one can partition thisintegration into integrations over the pulse separations ΔT₆ whereuponthe symbol estimates {circumflex over (Z)}_(i) have different values forthe correlation coefficients c(δi). The signal detection correlationmatrix R is constructed from the set of correlation coefficients {c(δi)}by the equation of definition R=[R(i,k)]=[c(k−i)] and is an n×n matrixfor full symbol T_(s) integration and an (n+n_(p)−1)×(n+n_(p)−1) matrixfor partial symbol ΔT_(s) integration where n is the number of datasymbols and the notation “n×n” reads “n by n”. Correlation coefficientsfor n_(p)=4 pulses are the values of the correlation function plotted inFIG. 5.

Equations (8) constructs a block length n=5, n_(p)=2 pulses, pulselength T_(s) example of the correlation matrix R for FIG. 8 for fullsymbol integration over the T_(s) pulse length specified by theparameter set T_(s), n, n_(p).

$\begin{matrix}{{{Signal}\mspace{14mu}{detection}\mspace{14mu}{correlation}\mspace{14mu}{matrix}}{1.\mspace{14mu}{Correlation}\mspace{14mu}{matrix}\mspace{14mu} R\mspace{14mu}{definition}}\text{}\mspace{31mu}\begin{matrix}{{R\left( {i,k} \right)} = {R\left( {{row},{column}} \right)}} \\{= {R\left( {{output},{input}} \right)}} \\{= {\left\lbrack {c\left( {\delta\; i} \right)} \right\rbrack\mspace{14mu}{matrix}\mspace{14mu}{with}\mspace{14mu}{elements}\mspace{14mu}{c\left( {\delta\; i} \right)}}} \\{= {n \times n\mspace{14mu}{matrix}\mspace{14mu}{for}\mspace{14mu} T_{s}\mspace{14mu}{integration}}} \\{= {\left( {n + n_{p} - 1} \right) \times \left( {n + n_{p} - 1} \right)\mspace{14mu}{matrix}}} \\{{\;}{{for}\mspace{14mu}\Delta\; T_{s}\mspace{14mu}{integration}}}\end{matrix}{{2.\mspace{14mu} R\mspace{14mu}{for}\mspace{14mu} T_{s}},{n = 5},{n_{p} = 2}}\mspace{34mu}{R = \begin{bmatrix}1 & 0.5 & 0 & 0 & 0 \\0.5 & 1 & 0.5 & 0 & 0 \\0 & 0.5 & 1 & 0.5 & 0 \\0 & 0 & 0.5 & 1 & 0.5 \\0 & 0 & 0 & 0.5 & 1\end{bmatrix}}} & (8)\end{matrix}$

In equations (8) in 1 the data symbols for the array of n transmitted Txpulses is the n×1 column vector Z with components {Z_(i)} and where[(o)]′ is the transpose of [(o)]. In 2 components of the n×1 detectedsignal vector Y=[Y₁, Y₂, . . . , Y_(n)]′ are equal to Y_(i)=X_(i)+n_(i)introduced in the previous. In 3 the matrix equation for Y is definedwhere R is the correlation matrix and U is the n×1 Rx noise vector. Thedefinition E{UU′}=2σ²R enables the ML solution of 3 to be derived{circumflex over (Z)}=[R′(2σ²R)⁻¹R]⁻¹R(2σ²R)⁻¹Y and simplified to theequivalent equation in 4 where {circumflex over (Z)} is the estimate ofZ and σ is the one-sigma value of the Rx additive white Gaussian noiseAWGN for each Rx detected data symbol.

$\begin{matrix}{{M\; L\mspace{14mu}{symbol}\mspace{14mu}{detection}\mspace{14mu}{for}\mspace{14mu} Q\; L\; M}{1.\mspace{14mu}\begin{matrix}{Z = \left\lbrack {Z_{i},Z_{2},\;\ldots\mspace{14mu},Z_{n}} \right\rbrack^{\prime}} \\{= \left\lbrack {{A_{1}{\exp\left( {j\;\varphi_{1}} \right)}},{A_{2}{\exp\left( {j\;\varphi_{2}} \right)}},\;\ldots\mspace{14mu},{A_{n}{\exp\left( {j\;\varphi_{n}} \right)}}} \right.}\end{matrix}}{{{2.\mspace{14mu} Y_{i}} = {X_{i} + {n_{i}\mspace{14mu}{for}\mspace{14mu}{all}\mspace{14mu} i}}},{X_{i} = {\Sigma_{\delta\; i}Z_{i + {\delta\; I}}{c\left( {\delta\; i} \right)}}}}{{3.\mspace{14mu} Y} = {{RZ} + U}}{{4.\mspace{14mu}\hat{Z}} = {R^{- 1}Y}}} & (8)\end{matrix}$A similar matrix inversion algorithm can be derived for the recovery ofestimates {circumflex over (Z)} of the transmitted symbol set using theset of signal detection measurements over ΔT_(s).

For step 2 consider a trellis symbol algorithm in FIG. 9 using a MLdecisioning metric or a MAP decisioning metric disclosed in patentapplication Ser. No. 10/772,597 or another decisioning metric. FIG. 9Ais the top level block diagram of the trellis algorithm for anon-iterative application. Basic elements of the algorithm are thetrellis parameters 170, trellis algorithm 171 structured by theparameter set in 170, and the trellis decoding algorithm 172. Thetrellis algorithm completes or partially completes trellis demodulationbefore handing off the data symbol estimates and metrics to the trellisdecoding algorithm 172 or alternatively, interleaves the trellis errorcorrection decoding 172 with trellis demodulation by accepting one ormore data symbol estimates from the trellis algorithm for decodingbefore returning 173 to the trellis algorithm for processing the nextdata symbols. Decoding data estimates 174 are handed off to the receiverfor further processing. The parameter set 170 is applicable to the idealpulse modulation defined in FIG. 5,8 with time as the differentiatingparameter as well as to the pulse waveforms in FIG. 6,7 and to otherapplications with other differentiating parameters. The correlationfunction in FIG. 5 for the pulse waveform in FIG. 8 has zero sidelobeswhich means only the mainlobe correlation has to be considered in thetrellis algorithm. Mainlobe correlation values for n_(p)=4 are plottedin FIG. 5. It is sufficient to use a one-sided correlation functionsince the correlation is symmetrical about the origin whereupon thecorrelation vector C whose elements are the mainlobe correlationcoefficients is observed to be equal toC=[c(0),c(1),c(2),c(3)]=[1,3/4,1/2,1/4] for n_(p)=4 where thecorrelation coefficients are c(0),c(1),c(2),c(3). Other trellisparameters are the number of data symbols n, number of parallel QLMchannels n_(p), number of data symbol states n_(s), and the number oftrellis states n_(t)=n₃^(2n_(p)−2)=2^b_(s)(2n_(p)−2) whereinn_(s)=2^b_(s)=4,8,16,64,356 for 4-PSK,8-PSK,16-QAM,64-QAM,256-QAM forthe correlation function in FIG. 5.

FIG. 9B uses the trellis parameters 170 in the initialization 150 priorto the start k=0 with an empty shift register SR which normally containsthe 2n_(p)−1 Rx correlated data symbols for the mainlobe plus thecorrelated symbols for the sidelobes for each of the possible trellispaths. At k=0 the path metric α₀(xi) is set equal to a negative or zeroinitialization constant for all of the nodes xi=0,1,2, . . . ,(n_(s)^(2np−2)−1} of the trellis diagram where α₀(xi) is the logarithmof the state S₀ path metric at k=0 for node xi, n_(s) is the number ofstates of the data symbol modulation, the Rx symbols are indexed over kwith k=0 indicating the initial value prior to the Rx symbol k=1, nodesof the trellis diagram are the states of the SR, and state S_(k) refersto the trellis diagram paths and metrics at symbol k in the trellisalgorithm. In the previous for ML block decoding the symbols wereindexed over i.

Loop 151 processes the Rx symbols k=1,2, . . . , n where the index kalso refers to the corresponding algorithm steps and to the states ofthe trellis algorithm. In 152 the Rx signals are pulse detected toremove the carrier frequency and waveform to recover a normalizedcorrelated data symbol Y_(k). For each Rx symbol Y_(k) the statetransition decisioning metrics R_(k)(jxi) are calculated by thelogarithm transition metric equations {R_(k)(jxi)=−|Y_(k)−{circumflexover (X)}_(k)(jxi)|^2} for a ML metric, {R_(k)(jxi)=|{circumflex over(x)}_(k)|^2−2Real(Y_(k){circumflex over (X)}_(k)(jxi))*} for a MAPmetric wherein (o)* is the complex conjugate of (o), and{R_(k)(jxi)=metric(Y_(k),{circumflex over (X)}_(k))} for another metric,for all possible transition paths {jxi} from the previous stateS_(k−1)(xi) at node xi to the new state S_(k)(jx) at node jx in thetrellis diagram snd where {circumflex over (X)}_(k)(jxi) is thehypothesized normalized detected correlated symbol k for the path jxi.For a mainlobe correlation function the {circumflex over (X)}_(k)(jxi)is defined by the equation {circumflex over (X)}_(k)(jxi)=c(n_(p)−1)[sr(1)+sr(2n_(p)−1)]+ . . . +c(1) [sr(n_(p)−1)+sr(n_(p)+1)]+c(0)[sr(n_(p))] which calculates {circumflex over (X)}_(k)(jxi) as thecorrelated weighted sum of the elements of the shift registerSR=[sr(1),sr(2), . . ., sr(2n_(p)−1)]′ with {circumflex over(Z)}_(k)=sr(n_(p)),{circumflex over (Z)}_(k−1)=sr(n_(p)−1), {circumflexover (Z)}_(k+1)==sr(n_(p)+1), . . . where c(0)=1, the normalized datasymbol estimates {{circumflex over (Z)}_(k)} correspond to thetransition index jxi, and the state k estimated symbol {circumflex over(Z)}_(k) is the SR center element sr(n_(p)) with correlation coefficientc(0)=1. Symbols move from left to right starting with “j” with each newreceived symbol or step in the trellis recursion algorithm, and endingwith “i”. With this convention “j” is indexed over the states of sr(1),“x” is indexed over the current states of sr(2), . . . ,sr(2n_(p)−2),and “i” is indexed over the states of sr(2n_(p)−1). Index over the pathsof the trellis diagram is defined by the equation jxi=sr(1)+n_(s)sr(2)+n_(s) ^2 sr(3)+ . . . +n_(s)^(2n_(p)−2) sr(2n_(p)−1)=0,1,2, . . ., n_(s)^(2n_(p)−1)−1 when the contents of the SR elements are theindices corresponding to the assumed data symbol state values.

Loop 153 calculates the best trellis transition paths from state S_(k−1)to the new state S_(k) for the new nodes jx=0,1,2, . . . ,n_(s)^(2n_(p)−2)−1. In 154 the path metric α_(k)(S_(k)) is defined bythe recursive logarithm equationα_(k)(S_(k))=α_(k−1)(S_(k−1))+R(S_(k−1)−>S_(k)) which can be rewrittenas α_(k)(jx)=α_(k−1)(xi)+R(jxi) since the state S_(k) corresponds tonode jx, state S_(k−1) corresponds to node xi and the state transitionfrom S_(k−1) to S_(k)represented symbolically as S_(k−1)−>S_(k)corresponds to the path jxi.

The best path metric α_(k)(jx) for each new node jx is chosen by thedecisioning equation α_(k)(jx)=maximum{α_(k−1)(xi)+R_(k)(jxi)} withrespect to the admissible xi. For each jx, the corresponding xi yieldingthe highest value of the path metric α_(k)(jx) is used to define the newsymbol {circumflex over (Z)}_(k) and path.

For k≧D the state metric S_(k) is upgraded for this new path jxi by theupdate operation S_(k)(:,jx)=[{circumflex over (Z)}_(k)(jxi);S_(k−1)(1:D−1, xi)] using Matlab notation which replaces the column jxvector with the column xi vector after the elements of xi have beenmoved down by one symbol and the new symbol {circumflex over (Z)}_(k)added to the top of the column vector which is the row 1 element. StateS_(k) is a D by (n₁₀₁^(2n_(p)−2) matrix with the column vectors equal tothe trellis states over the past D symbols where “D” is the trellisdecoding memory extending over several correlation lengths (2n_(p)−1)for the solution to be stabilized. In Matlab notation the S_(k)(:,jx) isthe column vector jx of S_(k) consisting of the new symbol {circumflexover (Z)}_(k) and the previous D−1 symbols along the trellis path tonode jx and the S_(k−1)(1:D,xi) is the D×1 column vector of S_(k−1) forthe previous node xi.

For k≦D the state metric S_(k) is upgraded for this new path jxi by theoperation S_(k)(:;jx)=[{circumflex over (Z)}_(k)(jxi); S_(k−1)(:;xi)]which replaces the column jx vector with the column xi vector after thenew symbol {circumflex over (Z)}_(k) has been added to the top of thecolumn which is the row 1 element to increase the path size by one.State S_(k) is a k by (n₁₀₁^(2n_(p)−2) matrix with the column vectorsequal to the trellis states over the past k symbols.

Metric values for each path in S_(k) are stored for later use in softdecisioning turbo and convolutional decoding. Metrics of interest foreach symbol k and for each jx are the values of {α_(k−1)(xi)+R(jxi)} forall admissible xi states for the new path symbol {circumflex over(Z)}_(k) for jx for k.

For symbols k≧D the best path jx is found which maximizes α_(k)(jx) andthe estimated value {circumflex over (Z)}_(k−D) for symbol k−D is thelast row element of the column corresponding to this best path in statemetric S_(k). This continues until k=n and ends the jx loop 153 and thek loop 151.

Processing 162 continues with steps k=n+1, . . . ,n+D−1 160,161 torecover the estimated values {circumflex over (Z)}_(k−D) of the Txsymbols Z_(k) which are read from the corresponding row elements D−1,D−2, . . . , 1 of the column in the state metric S_(n) corresponding tothe best path jx found for the last symbol k=n. This ends the jx loop161.

Outputs 164 of the trellis algorithm used for trellis decoding are theestimates {{circumflex over (Z)}_(k)} of the transmitted symbols {Z_(k)}and the corresponding metric values for all admissible states for eachnew path symbol {circumflex over (Z)}_(k) for all k. Trellis errorcorrection turbo or convolutional decoding 165 recovers data estimatesand hands off the data estimates 166 to the receiver for furtherprocessing.

The trellis algorithm for QLM example FIG. 9 using partial symbol ΔT_(s)integration presents another approach to a trellis algorithm for symbolrecovery which offers a potential reduction in computational complexitycompared to the algorithm for full symbol T_(s) integration in thetrellis algorithm in FIG. 9. The largest computational burden is thecalculation of the metrics, paths, and states. For the trellis algorithmin FIG. 9 the number of calculations is essentially determined by thenumber n_(s)^(2n_(p)−2) of nodes in the trellis algorithm. For theΔT_(s) integration in the trellis algorithm the number of nodes reducesto a significantly lower number n_(s)^(n_(p)−1). For this inventiondisclosure it is sufficient to demonstrate the trellis algorithm definedin FIG. 9.

FIG. 10 measures the trellis decoding performance for uncoded 4-PSKn_(p)=1 and for n_(p)=2 layers of QLM modulation implementing thedecoding algorithm FIG. 9. Performance is plotted as bit error rate BERversus the normalized value (E_(b)/N_(o))/n_(p) of the E_(b)/N_(o) forthe new bound from equation (4). Normalization means that for a givenBER the (E_(b)/N_(o))/n_(p) has the same value for all n_(p). Forexample, this means that BER=0.001 requires (E_(b)/N_(o))/n_(p)=6.8 dBand for n_(p)=1,2,4 this requires E_(b)/N_(o)=6.8+0=6.8, 6.8+3=9.8,6.8+6=12.8 dB respectively. Measured performance values for n_(p)=2 arefrom a direct error count Monte Carlo simulation of the trellisalgorithm and are plotted in FIG. 10 as discrete measurement points.

For step 2 consider an iterative trellis symbol algorithm in FIG. 11.The correlation function observed in FIG. 6, 7 for OWFMA, OFDMAwaveforms have sidelobes which cause a degradation in BER performanceunless they are incorporated into the trellis algorithm. A method forreducing this loss of BER performance without increasing the number oftrellis states is to use an iterative algorithm which calculates theestimated data symbols in the first iteration using part or all of themainlobe correlation function, uses these estimates to fill in thecontributions of the sidelobes in the calculation of the estimated datasymbols in the second iteration of the trellis algorithm, and continuesthis iteration if necessary.

FIG. 11 is a flow diagram of an interative trellis symbol algorithmwherein the iteration is used to incorporate the effects of thesidelobes of the correlation function into the trellis state transitionmetric function R_(k)(jxi) in 152 in FIG. 9B in the non-iterativetrellis symbol algorithm with a relatively small increase incomputational complexity. In FIG. 9 the algorithm is initialized withthe parameter set in 176 which is the parameter set in 170 in FIG. 9Awith the partitioning of the correlation vector C into the mainlobevector C₀ plus the sidelobe vector C₁ and adding the specification ofthe stopping rule for the iterations. For a correlation vectorC=[c(0),c(1), . . . , c(n_(p)−1),c(n_(p)), . . . , c(n_(c))] consistingof n_(c) correlation coefficients, the mainlobe vector is C₀=[c(0),c(1),. . . ,c(n_(p)−1), 0,0, . . . ,0] and the sidelobe vector is C₁=[0,0, .. . , 0,c(n_(p)), . . . , c(n_(c))] which partitions C into the vectorsum C=C₀+C₁.

The iterative algorithm starts 177 by implementing the trellis algorithm171 in FIG. 9A for the correlation mainlobe using the non-zero C₀coefficients. Output data symbol estimates are used to calculate thea-priori estimated sidelobe contribution {circumflex over (X)}_(k|1) in179 to {circumflex over (X)}_(k)(jxi) which is the hypothesizednormalized detected correlated symbol k for the path jxi in thecalculation of the metric R_(k)(jxi) in 152 in FIG. 9B. In thisimplementation 180 of the trellis algorithm 152,154 in FIG. 9B, the{circumflex over (X)}_(k)(jxi)={circumflex over(X)}_(k|0)(jxi)+{circumflex over (X)}_(k|1) is the sum of thehypothesized mainlobe contribution {circumflex over (X)}_(k|0)(jxi)using the non-zero C₀ coefficients as described in FIG. 9 and thesidelobe contribution {circumflex over (X)}_(k|1) using the data symbolestimates from 177 and the non-zero C₁ coefficients and wherein thesubscripts “k|0” reads “index k given C₀” and “k|1” reads “index k givenC₁”. From 152 in FIG. 9B we find the {circumflex over (X)}_(k|0)(jxi) isdefined by the equation {circumflex over (X)}_(k|0)(jxi)=c(n_(p)−1)[sr(1)+sr(2n_(p)−1)]+ . . . +c(1) [sr(n_(p)−1)+sr(n_(p)+1)]+c(0)[sr(n_(p))] which calculates {circumflex over(X)}_(k|0)(jxi)={circumflex over (X)}_(k)(jxi) in FIG. 9B as thecorrelated weighted sum of the elements of the shift registerSR=[sr(1),sr(2), . . . , sr(2n_(p)−1)]′ with {circumflex over(Z)}_(k)=sr(n_(p)),{circumflex over (Z)}_(k−1)=sr(n_(p)−1), {circumflexover (Z)}_(k+1)=sr(n_(p)+1), . . . where c(0)=1, the normalized datasymbol estimates {{circumflex over (Z)}_(k)} correspond to thetransition index jxi, and the state k estimated symbol {circumflex over(Z)}_(k) is the SR center element sr(n_(p)) with correlation coefficientc(0)=1. Symbols move from left to right starting with “j” with each newreceived symbol or step in the trellis recursion algorithm, and endingwith “i”. With this convention “j” is indexed over the states of sr(1),“x” is indexed over the current states of sr(2), . . . , sr(2n_(p)−2),and “i” is indexed over the states of sr(2n_(p)−1). Index over the pathsof the trellis diagram is defined by the equation jxi=sr(1)+n_(s)sr(2)+n_(s)^2 sr(3)+ . . . +n_(s)^(2n_(p)−2) sr(2n_(p)−1)−1=0,1,2, . . ., n_(s)^(2n_(p)−1)−1 when the contents of the SR elements are theindices corresponding to the assumed data symbol state values. Thesidelobe contribution is equal to {circumflex over(X)}_(k|1)=c(n_(p))({circumflex over (Z)}_(k−n) _(p) +{circumflex over(Z)}_(k+n) _(p) )+c(n_(p)+1) ({circumflex over (Z)}_(k−1−n) _(p)+{circumflex over (Z)}_(k+1+n) _(p) )+c(n_(p)+2) ({circumflex over(Z)}_(k−2−n) _(p) +{circumflex over (Z)}_(k+2+n) _(p) )+ . . . until theend of the sidelobe correlation coefficients or the end of the datasymbol estimates and wherein {circumflex over (Z)}_(k−n) _(p) is thedata symbol estimate in 179 for symbol k−n_(p).

Output of this modified trellis algorithm 180 is the set of data symbolestimates. A stopping rule in 176 is used to decide 182 if anotheriteration is required. When another iteration is required the datasymbol estimates are used 184 to update the calculation 179 of thea-priori contribution {circumflex over (X)}_(k|1) of the sidelobes tothe {circumflex over (X)}_(k)(jxi) in the modified trellis algorithm180. With no further iteration the trellis error correction decoding 183implements the trellis error correction decoding 172 in FIG. 9A, handsoff the data estimates 186 to the receiver for further processing. andreturns 185 to the trellis algorithm for processing the next data symbolor symbols when the trellis error correction decoding 183 is interleavedwith the trellis demodulation. Alternatively, the trellis demodulationis completed or partially completed before handing off the data symbolestimates and metrics to the trellis decoding algorithm 183.

For step 2 a method to reduce the number of trellis states is to use asequential trellis bit algorithm. With this method the data symbol bitsare individually estimated by a trellis algorithm over the correlationfunction using the corresponding bits of each data symbol for eachtrellis pass. A comparison of the number of trellis states n_(t) for thesymbol and bit algorithms is given in 1,2 in equations (9). This numbern_(t) of trellis states is required to support each step k of thetrellis demodulation and there are n_(p) demodulation steps in each datasymbol interval T_(s) which means the number of trellis states per T_(s)second interval is equal to n_(p)n_(t). The number of trellis statesrequires a SR length 2n_(p)−2 and is equal to n_(s)^(2n_(p)−2) whereasthe number of trellis paths requires a SR length 2n_(p)−1 and is equalto n_(s)^(2n_(p)−1). The computational complexity of a trellis algorithmis driven by the number of trellis states.

$\begin{matrix}{{{Number}\mspace{14mu}{of}\mspace{14mu}{trellis}\mspace{14mu}{states}{\mspace{11mu}\;}n_{t}}{1.\mspace{14mu}{Trellis}\mspace{14mu}{symbol}\mspace{14mu}{algorithm}\mspace{14mu}{trellis}\mspace{14mu}{states}}\begin{matrix}{\mspace{31mu}{n_{t} = {n_{s}\hat{}\left( {{2\; n_{p}} - 2} \right)}}} \\{= {2\hat{}{b_{s}\left( {{2\; n_{p}} - 2} \right)}}}\end{matrix}{2.\mspace{14mu}{Trellis}\mspace{14mu}{bit}\mspace{14mu}{algorithm}\mspace{14mu}{trellis}\mspace{14mu}{states}}\mspace{34mu}{n_{t} = {b_{s}{2\hat{}\left( {{2\; n_{p}} - 2} \right)}}}} & (9)\end{matrix}$

FIG. 12,13 calculate the number of trellis states n_(t) for theinformation bits b per data symbol interval for values to b=12Bits/Hz=Bits/(Symbol Interval) for the trellis symbol demodulationalgorithm and the trellis bit demodulation algorithm respectively usingequations (9) to calculate the number of trellis states and calculatingthe information bits b vs. n_(p) performance for PSK and QAM from FIG.3,4. For trellis symbol demodulation, FIG. 12 calculates the number oftrellis states n_(t) vs. b for 4-PSK in 200, 8-PSK in 201, 16-QAM in202, 64-QAM in 203, and 256-QAM in 204. For trellis bit demodulation,FIG. 13 calculates the number of trellis states n_(t) vs. b for 4-PSK in205, 8-PSK in 206, 16_QAM in 207, 64-QAM in 208, and 256-QAM in 209.FIG. 13 compared to FIG. 12 illustrates a reduction in computationalcomplexity using the trellis bit demodulation algorithm compared to thetrellis symbol demodulation algorithm.

In FIG. 13 the number of bit passes is equal to the number of modulationbits b_(s) per data symbol which number multiplies the number of trellisstates to calculate the equivalent number of trellis states for the bitalgorithm. The data symbol rate reduction required to implement the biterror correction decoding is not factored into these plots since therequired code rates are expected to be relatively high and have not beenestablished. With the bit algorithm the complexity of the data symbolmodulation may require the simultaneous demodulation of more than onebit for each data symbol in order to reduce the bit(s) decisioning lossand this could increase the complexity of the bit algorithm. Also notfactored into these plots is the impact of the differences in the n_(p)over the T_(s) interval for the same values of b since the number ofdata symbol modulations is equal to n_(p)n_(t) over a T_(s) interval forthe same values of b.

FIG. 14 illustrates the decisioning manifolds and bit sequencing for QLM8-PSK demodulation using a trellis bit detection algorithm. In 190 the8-PSK data symbol modulation is mapped onto a unit circle in the complexplane using the binary representation b₀b₁b₂ for the b_(s)=3 bit phasestates n_(s)=8=2^(3 bit) with the zero state 191 equal to b₀b₁b₂=000.The 8-PSK phase states are arranged as a Gray code with the third bitb₂=0,1 values on the respective bit b₀,b₁ decisioning boundaries 195,199of their manifolds in the complex plane to reduce the impact of theundecided bit b₂ on the decisioning performance of b₀, b₁. It is wellknown that the Gray code reduces the probability of a multibit error andthe BER for a given data symbol error since the neighboring symbolsdiffer from each other by only one bit position.

In 192 the decisioning manifolds for the first bit b₀ are the respectivesubspaces of the complex plane 194 with real axis x and complex axis jywherein j=√(−1), specified by b₀=0 decisioning 193 and b₁=1 decisioning193 with the decisioning boundary 195 separating the manifolds. In 196the decisioning manifolds for the second bit b₁ are the respectivesubspaces of the complex plane 198 specified by b₁=0 decisioning 197 andb₁=1 decisioning 197 with the decisioning boundary 199 separating themanifolds. In 196 the bit b₁ decisioning is conditioned on the knowledgeof the first bit b₀ being b₀=0,1. This means for b₀=0 the decisioningmanifolds in 196 are restricted to the b₀=0 manifold in 192 and for b₀=1to the b₀=1 manifold in 192.

FIG. 15 is a flow diagram of a trellis bit demodulation algorithm withcorrelated bit error correction encoding and decoding. The algorithm isinitialized with the parameter set in 210 which is the parameter set 170in FIG. 9A with the identification of the bit representation b₀b₁b₂ . .. b_(s−1) of the b_(s) bit trellis states for the data modulation anddefinition of the corresponding decisioning boundaries and metrics forcalculation of the trellis state transition metric R_(k)(jxi) in 152 inFIG. 9B in the trellis symbol algorithm.

The trellis bit algorithm 211 implements the trellis symbol algorithm inFIG. 9 with the symbols reduced to the first bit b₀ for each of thecorrelated data symbols to initiate the algorithm in the first trellispass, implements the data symbol words b₀b₁ for the next trellis passwith the bits b₀ estimated from the first pass, and so forth until thecomplete data symbol words b₀b₁b₂ . . . b_(s−1) have been recovered. Ineach pass the trellis state transition metric R_(k)(jxi) in 152 in FIG.9B in the trellis symbol algorithm is calculated using the definition ofthe corresponding decisioning boundaries and metrics in 210 followingthe procedure outlined in FIG. 14 for 8-PSK and the estimated bit valuesfrom the previous trellis passes.

Bit estimates from the trellis bit algorithm are error correctiondecoded and re-encoded 213 to correct the decisioning errors resultingfrom a combination of noise and the non-optimal nature of the bitdecisioning metrics. Bit decisioning metrics are non-optimal when thereare unknown higher order bits which are undefined since the multi-layercorrelations of the parallel QLM channels introduce random fluctuationscontributed by these higher order bits. The error correction code findsthe correct bit sequence and then regenerates the original encoded bitsequence to enable the next bit pass to be implemented with a relativelyclean estimate of the bits in the previous pass. This bit errorcorrection is intended to improve the performance of the trellis bitalgorithm. Depending on the tolerance to performance loss this bit errorcorrection can be deleted to avoid the relatively small loss incommunications capacity due to the anticipated relatively high rate ofthe bit encoder.

The sequencing continues 214 when there is another bit to be processedwhereupon the corrected bit estimate from the bit error correction 213is handed off 216 to the trellis bit algorithm 211 for the next pass.When the next-to-last bit has been estimated and corrected by the biterror correction 213 the algorithm stops the sequencing 212 and handsoff the estimated data symbols and metrics 217 to the trellis decoding215 which implements the trellis error correction decoding 172 in FIG.9A, hands off the bit estimates 219 to the receiver for furtherprocessing, and returns 218 to the trellis algorithm for the processingof the next data symbol or symbols. Alternatively, the trellisdemodulation is completed or partially completed before handing off thedata symbol estimates and metrics to the trellis decoding algorithm 215.

FIG. 16 is a flow diagram of an interative trellis bit algorithm whereinthe iteration is used to incorporate the effects of the sidelobes of thecorrelation function into the trellis state transition metric R_(k)(jxi)in 152 in FIG. 9B in the non-iterative trellis symbol algorithm with arelatively small increase in computational complexity. In FIG. 16 thealgorithm is initialized with the parameter set in 220 which is theparameter set in 210 in FIG. 15 with the partitioning of the correlationvector C into the mainlobe vector C₀ plus the sidelobe vector C₁ andadding the specification of the stopping rule for the iterations. For acorrelation vector C=[c(0),c(1), . . . , c(n_(p)−1),c(n_(p)), . . . ,c(n_(c))] consisting of n_(c) correlation coefficients, the mainlobevector is C₀=[c(0),c(1), . . . , c(n_(p)−1),0,0, . . . , 0] and thesidelobe vector is C₁=[0,0, . . . , 0,c(n_(p)), . . . , c(n_(c))] topartition C=C₀+C₁.

The iterative algorithm starts 221 by implementing the trellis algorithm171 in FIG. 9A with the symbols reduced to the first bits b₀ for thecorrelation mainlobe using the non-zero C₀ coefficients. Output bitestimates from the trellis bit algorithm 221 are used to calculate thea-priori estimated sidelobe contribution {circumflex over (X)}_(k|1) in223 to {circumflex over (X)}_(k)(jxi) which is the hypothesizednormalized detected correlated symbol k for the path jxi in thecalculation of the metric R_(k)(jxi) in 152 in FIG. 9B. In thisimplementation 224 of the trellis algorithm 171 in FIG. 9A, the{circumflex over (X)}_(k)(jxi)={circumflex over(X)}_(k|0)(jxi)+{circumflex over (X)}_(k|1) is the sum of thehypothesized mainlobe contribution {circumflex over (X)}_(k|0)(jxi)using the non-zero C₀ coefficients as described in FIG. 9 and thesidelobe constibution {circumflex over (X)}_(k|1) using the bitestimates from 221 and the non-zero C₁ coefficients and wherein thesubscripts “k|0” reads “index k given C₀” and “k|1” reads “index k givenC₁”. From 152 in FIG. 9B we find the {circumflex over (X)}_(k|0)(jxi) isdefined by the equation {circumflex over (X)}_(k|0)(jxi)=c(n_(p)−1)[sr(1)+sr(2n_(p)−1)]+ . . . +c(1) [sr(n_(p)−1)+sr(n_(p)+1)]+c(0)[sr(n_(p))] which calculates {circumflex over(X)}_(k|0)(jxi)={circumflex over (X)}_(k)(jxi) in FIG. 9B as thecorrelated weighted sum of the elements of the shift registerSR=[sr(1),sr(2), . . . , sr(2n_(p)−1)]′ with {circumflex over(Z)}_(k)=sr(n_(p)),{circumflex over (Z)}_(k−1)=sr(n_(p)−1),{circumflexover (Z)}_(k+1)=sr(n_(p)+1), . . . where c(0)=1, the normalized datasymbol estimates {{circumflex over (Z)}_(k)} correspond to thetransition index jxi, and the state k estimated symbol {circumflex over(Z)}_(k) is the SR center element sr(n_(p)) with correlation coefficientc(0)=1. Symbols(bits) move from left to right starting with “j” witheach new received symbol or step in the trellis recursion algorithm, andending with “i”. With this convention “j” is indexed over the states ofsr(1), “x” is indexed over the current states of sr(2), . . . ,sr(2n_(p)−2), and “i” is indexed over the states of sr(2n_(p)−1). Indexover the paths of the trellis diagram is defined by the equationjxi=sr(1)+n_(s) sr(2)+n_(s)^2 sr(3)+ . . . +n_(s)^(2n_(p)−2)sr(2n_(p)−1)−1=0,1,2, . . . , n_(s)^(2n_(p)−1)−1 when the contents ofthe SR elements are the indices corresponding to the assumed data symbolstate values. The sidelobe contribution is equal to {circumflex over(X)}_(k|1)=c(n_(p)) ({circumflex over (Z)}_(k−n) _(p) +{circumflex over(Z)}_(k+n) _(p) )+c(n_(p)+1) ({circumflex over (Z)}_(k−1−n) _(p){circumflex over (Z)}_(k+1+n) _(p) )+c(n_(p)+2) ({circumflex over(Z)}_(k−2−n) _(p) +{circumflex over (Z)}_(k+2+n) _(p) )+ . . . until theend of the sidelobe correlation coefficients or the end of the datasymbol bit estimates and wherein {circumflex over (Z)}_(k−n) _(p) is thedata symbol bit estimate in 223 for symbol k−n_(p).

Output of this modified trellis bit algorithm 224 is the set of datasymbol bit estimates which are error correction decoded and re-encoded226 to correct the decisioning errors. A stopping rule in 227 is used todecide if another iteration is required. When another iteration isrequired the data symbol bit estimates are used 230 to update thecalculation 223 of the a-priori contribution {circumflex over (X)}_(k|1)of the sidelobes to the {circumflex over (X)}_(k)(jxi) in the modifiedtrellis algorithm 224. With no further iteration the next bit 228 isprocessed 225 by the trellis bit algorithm 221 whereupon the correctedbit estimate from the bit error correction 226 is used to generate thesidelobes 223 for the trellis bit algorithm 224 to begin the next set ofiterations. When the next-to-last bit has been estimates and correctedby the bit error correction 226 and the iteration algorithm completed227, the estimated data symbols and metrics are handed off to thetrellis error correction decoding 229 which implements the trellis errordecoding 172 in FIG. 9A, hands off the data estimates 232 to thereceiver for further processing, and returns 231 to the trellis bitalgorithm for processing the next data symbol or symbols when thetrellis error correction decoding 229 is interleaved with the trellisdemodulation. Alternatively, the trellis demodulation is completed orpartially completed before handing off the data symbol estimates andmetrics to the trellis decoding algorithm 229.

For step 2 there are several ways to reduce the computational complexityat the expense of some performance loss for the trellis symbol and bitalgorithms and the iterative trellis symbol and bit algorithms. A methodto reduce computational complexity is to reduce the number of trellisstates jx and transition paths jxi in 151, 152, 153, 154 in FIG. 9B inthe trellis algorithm by eliminating the trellis states and trellispaths in 154 in FIG. 9B which have relatively poor values of the pathmetric α_(k)(jx) used to define the new symbol {circumflex over (Z)}_(k)and path. A second method to reduced the computational complexity is toreduce the number of trellis states by eliminating the lower correlationvalues of the sidelobes and mainlobe. A third method to reduce thecomputational complexity is to modify the iterative algorithm tocalculate the forward trellis performance using the forward half of themainlobe and followed by a backward trellis algorithm using the otherhalf of the mainlobe wherein the trellis algorithm in FIG. 9 is aforward algorithm and the backward algorithm simply replaces the forwardrecursive metric equation α_(k)(jx)=α_(k−1)(xi)+R(jxi) with the backwardrecursive equation β_(k−1)(jx)=β_(k)(xi)+R(jxi) and runs the trellisalgorithm in reverse by proceeding with k, k−1, k−2, . . . and whereinβ_(k−1)(jx) is the backward state metric used to define the new symbol{circumflex over (Z)}_(k−1) and path as described in application Ser.No. 10/772,597. A fourth method to reduce the computational complexityit so change the forward-backward algorithm to incorporate techniques toeliminate the trellis state and trellis paths with relatively poorperformance metrics. These are examples of the various algorithms forreducing the computational complexity at the expense of reducing thedemodulation performance. Sequential demodulation techniques, partialsymbol and bit integration over ΔT_(s) and Δk intervals, and otherdemodulation techniques are available as potential candidates for QLMdemodulation. The present invention is not intended to be limited tothese QLM demodulation methods and techniques shown herein but is to beaccorded the wider scope consistent with the principles and novelfeatures disclosed herein.

OFDMA quadrature parallel-layered modulation QLM can increase the datarate either using timing offsets or using frequency offsets or using acombination of both, as the communications parameter which is changedbetween layers to allow separability of the layers and recovery of thelayered transmitted data in the receiver. OFDMA QLM with frequencyoffsets is implemented in FIG. 17 in a transmitter and in FIG. 20 in areceiver.

FIG. 17 is a transmitter block diagram modified to support OFDMA QLMwith frequency offsets to increase the symbol transmission rate from1/T_(s) to the QLM rate n_(p)/T_(s) and with an increase in transmitterpower to support this increased data rate. Ideal OFDMA modulates N inputdata symbols at the sample rate 1/T_(s) over the time interval NT_(s)with an N-point inverse fast fourier transform FFT⁻¹ to generated Nharmonic waveforms e^j2nkn/N with each modulated by the correspondingdata symbol wherein the normalized frequencies k=0,1, . . . N−1correspond to channels 0,1, . . . , N−1, “j”=√(−1), “n=pi”, and “n” is atime index,. Data symbol output rates are 1/NT_(s) per channel and the Nchannels have a total symbol rate equal to N/NT_(s)=1/T_(s)=B=(Nyquistsample rate). Signal processing starts with the stream of user inputdata words (d_(k)} 46 with k indexed over the words. Frame processor 47accepts these data words and performs turbo error correction encoding,error detection cyclic redundant encoding CRC, frame formatting, andpasses the outputs to the symbol encoder 48 which encodes the frame datawords into data symbols for handover to the OFDMA QLM signal processing.QLM transmits in parallel N received data symbols for each of the n_(p)FFT⁻¹ signal processing steams. Each set of received N data symbols areoffset in frequency by 0, Δk, 2Δk, . . . , (n_(p)−1)Δk with Δk=1/n_(p)using the normalized frequency index k and are implemented in 49 by thefrequency translation operator with FFT⁻¹ time sample index n. Followingthis frequency translation and FFT⁻¹ signal processing, the outputstreams of the OFDMA encoded symbols for the n_(p) frequency offsets aresummed 51 and waveform encoded. The output stream of up-sampled complexbaseband signal samples 52 {z(t_(i))} at the digital sample times t_(i)with digitization index i, is handed over to the digital-to-analogconverter DAC, and the DAC output analog signal z(t) is single sidebandSSB upconverted 52 to RF and transmitted as the analog signal v(t)wherein v(t) is the real part of the complex baseband signal z(t) at theRF frequency. Non-ideal OFDMA has a separation interval betweencontiguous FFT⁻¹ data blocks to allow for timing offsets and the riseand fall times of the channelization filter prior to the FFT⁻¹processing.

CDMA quadrature parallel-layered modulation QLM can increase the datarate either using timing offsets or using frequency offsets or using acombination of both, as the communications parameter which is changedbetween layers to allow separability of the layers and recovery of thelayered transmitted data in the receiver. CDMA QLM with frequencyoffsets is implemented in FIG. 18 in a transmitter and in FIG. 21 in areceiver. Using a Hybrid Walsh or a generalized Hybrid Walsh CDMAorthogonal channelization code developed in U.S. Pat. No. 7,277,382 andpatent application Ser. No. 09/846,410 localizes the frequency spread ofthe decoded CDMA signal so that it is feasible to use a trellisalgorithm for decoding. With timing offsets the CDMA block codes have tobe reshuffled so that the encoded data symbolsZ(n(k))=Σ_(u)Z(u)C(u,n(k)) over blocks k=0,1,2, . . . are groupedtogether for each n to ensure that the timing offsets are notintroducing unwanted cross-correlations between CDMA channels.

FIG. 18 is a transmitter block diagram modified to support CDMA QLM withfrequency offsets to increase the symbol transmission rate from 1/T_(s)to the QLM rate n_(p)/T_(s) and to increase the transmitter power levelto support this increased data rate. Signal processing starts with thestream of user input data words (d_(k)} 101 with k indexed over thewords. Frame processor 102 accepts these data words and performs theturbo error correction encoding, error detection cyclic redundantencoding CRC, frame formatting, and passes the outputs to the symbolencoder 103 which encodes the frame data words into data symbols forhandover to the CDMA QLM signal processing. Similar to OFDMA thefrequency translation is performed 104 and the output streams of theCDMA encoded 105 symbols for the n_(p) frequency offsets are summed 106and waveform encoded and the up-sampled output stream of complexbaseband signal samples 107 {z(t_(i))} at the digital sample times t_(i)with digitization index i, is handed over to the DAC and the DAC outputanalog signal z(t) is SSB upconverted 107 to RF and transmitted as theanalog signal v(t) wherein v(t) is the real part of the complex basebandsignal z(t) at the RF frequency.

OWDMA quadrature parallel-layered modulation QLM can increase the datarate either using timing offsets or using frequency offsets or using acombination of both, as the communications parameter which is changedbetween layers to allow separability of the layers and recovery of thelayered transmitted data in the receiver. OWDMA QLM with timing offsetsis implemented in FIG. 19 in a transmitter and in FIG. 22 in a receiver.OWDMA was developed in patent application Ser. No. 09/826,118. OWDMAgenerates a uniform bank of orthogonal Wavelet filters with the samespacing and symbol rate as OFDMA and with the advantage that theindividual channels remain orthogonal with timing offsets and are lesssensitive to frequency offsets.

FIG. 19 is a transmitter block diagram modified to support OWDMA QLMwith time offsets to increase the symbol transmission rate from 1/T_(s)to the QLM rate n_(p)/T_(s) and to increase the transmitter power levelto support this increased data rate. Signal processing starts with thestream of user input data words (d_(k)} 111 with k indexed over thewords. Frame processor 112 accepts these data words and performs theturbo error correction encoding, error detection cyclic redundantencoding CRC, frame formatting, and passes the outputs to the symbolencoder 113 which encodes the frame data words into data symbols forhandover to the OWDMA QLM transmit signal processing. The n_(p) timedelays 0, ΔT_(s), 2ΔT_(s), 3ΔT_(s), . . . , (n_(p)−1)ΔT_(s) whereinΔT_(s)=T_(s)/n_(p), are performed 114 and the output streams of theOWDMA waveform encoded 115 symbols for the n_(p) time delays are summed116 and passband waveform encoded and the up-sampled output stream ofcomplex baseband signal samples 117 {z(t_(i))} at the digital sampletimes t_(i) with digitization index i, is handed over to the DAC and theDAC output analog signal z(t) is single sideband SSB upconverted 117 toRF and transmitted as the analog signal v(t) wherein v(t) is the realpart of the complex baseband signal z(t) at the RF frequency.

Other communications applications include TDMA QLM and FDMA QLM.Frequency hopped FH QLM is a layered QLM modulation with multiple accessbeing provided by the FH on the individual hops. PPM QLM can be layeredwith QLM similar to QAM when the symbol modulation is replaced bypulse-position-modulation PPM. For GMSK QLM the transmitter is modifiedby the QLM symbol rate increase.

FIG. 20 is a receiver block diagram modified to support OFDMA QLM fromthe OFDMA QLM transmitter in FIG. 17. Receive signal processing for QLMdemodulation starts with the wavefronts 54 incident at the receiverantenna for the n_(u) users u=1, . . . , n_(u)≦N_(c) which are combinedby addition in the antenna to form the receive Rx signal {circumflexover (v)}(t) at the antenna output 55 where {circumflex over (v)}(t) isan estimate of the transmitted signal v(t) 52 in FIG. 17 that isreceived with errors in time Δt, frequency Δf, and phase Δθ. Thisreceived signal {circumflex over (v)}(t) is amplified and downconvertedto baseband by the analog front end 56, synchronized (synch.) in time tand frequency f, waveform removed to detect the received QLM signal atthe QLM symbol rate, inphase and quadrature detected (I/Q), andanalog-to-digital ADC converted 57. ADC output signal is demultiplexedinto n_(p) parallel signals 58 which are offset in frequency by 0, −Δk,−2Δk, . . . , −(n_(p)−1)Δk wherein Δk=1/n_(p) and processed by theFFT's. Outputs are trellis decoded 59 with an algorithm comparable tothe algorithm defined in FIG. 9 for QLM PSK. Outputs are furtherprocessed 60,61 to recover estimates {circumflex over (d)}_(k) of thetransmitted data d_(k) with k indexed over the data words.

FIG. 21 is a receiver block diagram modified to support CDMA QLM fromthe CDMA QLM transmitter in FIG. 18. Receive signal processing for QLMdemodulation starts with the wavefronts 121 incident at the receiverantenna for the n_(u) users u=1, . . . , n_(u)≦N_(c) which are combinedby addition in the antenna to form the receive Rx signal {circumflexover (v)}(t) at the antenna output 122 where {circumflex over (v)}(t) isan estimate of the transmitted signal v(t) 107 in FIG. 18 that isreceived with errors in time Δt, frequency Δf, and phase Δθ. Thisreceived signal {circumflex over (v)}(t) is amplified and downconvertedto baseband by the analog front end 123, synchronized (synch.) in time tand frequency f, waveform removed to detect the received QLM signal atthe QLM symbol rate, inphase and quadratue detected (I/Q), andanalog-to-digital ADC converted 124. ADC output signal is demultiplexedinto n_(p) parallel signals 125 which are offset in frequency by 0, Δk,2Δk, . . . , (n_(p)−1)Δk and processed by the CDMA decoders. Outputs aretrellis decoded 126 with an algorithm comparable to the algorithmdefined in FIG. 9 for QLM PSK. Outputs are further processed 127,128 torecover estimates of the transmitted data d_(k) wherein k is indexedover the data words.

FIG. 22 is the receiver block diagram modified to support OWDMA QLM fromthe OWDMA transmitter in FIG. 19. Receive signal processing for QLMdemodulation starts with the wavefronts 131 incident at the receiverantenna for the n_(u) users u=1, n_(u)≦N_(c) which are combined byaddition in the antenna to form the receive Rx signal {circumflex over(v)}(t) at the antenna output 132 where {circumflex over (v)}(t) is anestimate of the transmitted signal v(t) 117 in FIG. 19 that is receivedwith errors in time Δt, frequency Δf, and phase Δθ. This received signal{circumflex over (v)}(t) is amplified and downconverted to baseband bythe analog front end 133, synchronized (synch.) in time t and frequencyf, waveform removed to detect the received QLM signal at the QLM symbolrate, inphase and quadrature detected (I/Q) and analog-to-digital ADCconverted 134. ADC output signal is demultiplexed into n_(p) parallelsignals 135 which are offset in time by 0, ΔT_(s), 2ΔT_(s) , . . . ,(n_(p)−1)ΔT_(s) and processed by the OWDMA decoders. Outputs are trellisdecoded 136 with an algorithm comparable to the algorithm defined inFIG. 9 for QLM PSK. Outputs are further processed 137,138 to recoverestimates {circumflex over (d)}_(k) of the transmitted data d_(k)wherein k is indexed over the data words.

Consider the QLM modulation and demodulation algorithms andimplementation for GMSK. QLM increases the data rate by transmittingn_(p)>1 layers of data encoded Gaussian frequency pulses that are timesynchronized for transmission at T_(s)/n_(p), 2T_(s)/n_(p), . . . ,(n_(p)−1)T_(s)/n_(p) offsets respectively for layers 2,3, . . . ,(n_(p)−1) relative to the ground or 1^(st) layer of GMSK. This means thebit-rate increases from 1/T_(s) to n_(p)/T_(s) and the bit or symboltime remains the same at T_(s). The trellis algorithm in FIG. 9 iscombined with the Viterbi algorithm, with suitable modifications tomodel the architecture of the GMSK demodulator.

This patent covers the plurality of everything related to QLMgeneration, QLM demodulation, and data recovery of QLM and to thecorresponding bounds on QLM to all applications of QLM inclusive oftheory, teaching, examples, practice, and of implementations for relatedtechnologies. The representative transition metric and trellisalgorithms for QLM demodulation are examples to illustrate themethodology and validate the performance and are representative of allQLM demodulation algorithms including maximum likelihood ML, maximum aposteriori MAP, maximum a priori, finite field techniques, direct anditerative estimation techniques, trellis symbol and iterativw trellissymbol and with/without simplifications, trellis bit and iterativetrellis bit and with/without simplifications and with/without bit errorcorrection coding, and all other related algorithms whose principalfunction is to recover estimates of the transmitted symbols for QLMparallel layered modulation as well as data recovery related to QLM andthe QLM bounds.

Preferred embodiments in the previous description of modulation anddemodulation algorithms and implementations for QLM for the knownmodulations and demodulations and for all future modulations anddemodulations, are provided to enable any person skilled in the art tomake or use the present invention. The various modifications to theseembodiments will be readily apparent to those skilled in the art and thegeneric principles defined herein may be applied to other embodimentswithout the use of the inventive faculty. Thus, the present invention isnot intended to be limited to the embodiments shown herein but is to beaccorded the wider scope consistent with the principles and novelfeatures disclosed herein. Additional applications for QLM signalprocessing and bound include the plurality of information theorecticapplications with examples being radar, imaging, and media processing.

What is claimed is:
 1. A method for implementation of QuadratureParallel-Layered Modulation (QLM) in a communications transmitter forcommunications over the same frequency bandwidth of a carrier frequencyusing time offset as a differentiating parameter, said method comprisingthe steps: generating a communications signal over a frequency bandwidthat the data symbol rate n_(p)/T_(s) wherein 1) each data symbol isencoded with information and has the same waveform 2) the Nyquist ratefor the data symbol transmission is equal to 1/T_(s), 3) the Nyquistrate is equal to the bandwidth 1/T_(s) of the data symbol waveform andis the data symbol transmission rate 1/T_(s) which is sufficient totransmit all of the information in each data symbol, 4) n_(p) is theincrease in the Nyquist data rate supported by QLM, 5) this increase inNyquist data rate can be viewed as increasing to n_(p) the number ofparallel communications channels supported by QLM at the data symbolrate 1/T_(s), 6) timing offset ΔT_(s) equal to the data symbol spacingΔT_(s)=T_(s)/n_(p) is the differentiating parameter when viewing thisincrease in data symbol rate as parallel communications channels whichare independent since the QLM demodulation algorithm recovers the datasymbols and data symbol encoded information at the QLM data symbol raten_(p)/T_(s), 7) each of these parallel channels of communications has aunique timing offset which can be identified as the channel 1 datasymbols with no timing offset, channel 2 data symbols with ΔT_(s)offset, channel 3 data symbols with 2ΔT_(s) offset, and continuing tochannel n_(p) data symbols with (n_(p)−1)ΔT_(s) offset, 8) which meansone can transmit n_(p) parallel layers of communications channels overthe same frequency bandwidth and recover the information in a receiverwith a QLM demodulation algorithm, up-converting the QLM signal to aradio frequency RF, power amplifying, transmitting the RF QLM signalusing the communications transmitter, and receiving the transmitted RFQLM signal in a communications receiver, amplifying, down-converting,and QLM demodulating the received QLM signal following by decoding torecover the data symbol information.
 2. A method for implementation oforthogonal frequency division multiple access (OFDMA) QLM forcommunications using frequency offset as a differentiating parameter,said method comprising the steps: generating a first communicationssignal over a frequency bandwidth 1/T_(s) at a carrier frequency for afirst set of N channels by modulating a first stream of N data symbolsat a data symbol rate 1/T_(s) with an N-point inverse fast fouriertransform (FFT⁻¹) waveform over a FFT⁻¹ block length NT_(s) to generateN orthogonal frequency harmonics modulated with the respective datasymbols and which modulated harmonics are the N channels forcommunications, generating a second communications signal over the sameblock length over the same frequency bandwidth at the same carrierfrequency for a second set of N channels by modulating a second streamof N data symbols at a data symbol rate 1/T_(s) with the same FFT⁻¹waveform with a frequency offset Δk equal to Δk=1/n_(p) wherein “n_(p)”is the number of QLM sets of channels in said frequency bandwidth andFFT⁻¹ harmonics are e^j2π(k+Δk)n/N for normalized frequencies k=0,1, . .. N−1 corresponding to channels 0,1, . . . , N−1 wherein “j”=√(−1),“n=pi”, and “n” is a time index, for any additional sets of channels,continuing generation of communication signals over the same blocklength over the same frequency bandwidth at the same carrier frequencyby modulating additional streams of data symbols with the same waveformat the same data symbol rate as the first and second streams of datasymbols with frequency offsets increasing in each communication signalin increments of Δk=1/n_(p) until the n_(p) signals are generated forn_(p) QLM sets of channels, repeating this generation of the QLM signalfor the next FFT⁻¹ block length NT_(s) and continuing for subsequentblock lengths, transmitting and receiving said communications signalsover a QLM communications link consisting of the n_(p) QLM sets ofchannels, recovering data symbols of the communications signals in areceiver using a demodulation algorithm, and combining said algorithmwith error correction decoding to recover the transmitted informationwhereby frequency offset has been used as a differentiating parameter toenable QLM parallel sets of channels for communications over the samefrequency bandwidth at the same carrier frequency with a data symbolrate independent of the Nyquist rate, to be demodulated.
 3. The methodin claim 2 for implementation of orthogonal frequency division multipleaccess (OFDMA) QLM in a communications transmitter and a communicationsreceiver for communications using frequency offset as a differentiatingparameter, said method further comprising: constructing QLM parallelchannels or parallel groups of channels of communications for a QLMcommunications link over a frequency bandwidth of a carrier frequencywith a data symbol rate independent of the Nyquist rate, using one ormore data symbol modulations for the QLM communications channels, usingone or more differentiating parameters to enable the channel signals ofthe QLM link to be demodulated, implementing said demodulation using atrellis algorithm or maximum likelihood algorithm or anotherdemodulation algorithm combined with error correction decodingalgorithms, wherein said QLM demodulated signal in a communicationsreceiver has been generated in a communications transmitter,up-converted to a radio frequency RF, power amplified, and transmittedas a RF QLM signal in a communications transmitter, and received in saidcommunications receiver, amplified, down-converted, and QLM demodulatedfollowed by decoding to recover the data symbol information.
 4. A methodfor implementation of QLM demodulation for communications over the samefrequency bandwidth of a carrier frequency using time and/or frequencyand/or other offsets as the differentiating parameters and using trellissymbol demodulation, said method comprising the steps: receiving QLMdata symbols indexed on k=1,2, . . . , n for n data symbols, evaluatingcorrelation coefficients for received QLM data symbols, establishingtrellis states and trellis paths for each data symbol whereby a) thereare n_(s)^(2n_(c)−2) trellis states wherein “n_(s)” is the number ofstates of each data symbol, and “n_(c)” is the number of one-sidedcorrelation coefficients for symmetrical correlation functions, b) thereare n_(s)^(2n_(c)−1) trellis paths from trellis state S_(k−1) for datasymbol k−1 to a new trellis state S_(k) for data symbol k, c) indexjxi=0,1,2, . . . , n_(s)^(2n_(c)−1)−1 is a trellis path index fromS_(k−1) to S_(k) using n_(s)-ary index symbols jxi reading from left toright wherein “j” is an index for a new data symbol, “i” is an index fora last data symbol and “x” is a set of n_(s)-ary index data symbolsbetween “j” and “i”, d) index jx is over n_(s)^(2n_(c)−2) trellis statesS_(k)(jx), e) index xi is over n_(s)^(2n_(c)−2) trellis statesS_(k−1)(xi), f) creating a D row by n_(s)^(2n_(c)−2) column memory “M”for storing trellis path decisions wherein D is a multiple of n_(c),initializing the trellis algorithm for k=0 implementing the trellisalgorithm for each step k starting with k=1 by 1) evaluatinghypothesized values {circumflex over (X)}_(k)(jxi) of received QLMcorrelated data symbols for all paths jxi, 2) measuring a received QLMdata symbol Y_(k) for data symbol k, 3) evaluating a logarithm statetransition decisioning metric R(jxi) which is a function of {circumflexover (X)}_(k)(jxi) and Y_(k) for symbol k for all possible paths jxifrom S_(k−1)(xi) to S_(k)(jx), 4) finding a best path metric α_(k)(jx)and corresponding path jxi from S_(k−1)(xi) to S_(k)(jx) by using alogarithm decisioning equation α_(k)(jx)=max{α_(k−1)(xi)+R_(k)(jxi)}which finds xi that maximizes “max” the sum “α_(k−1)(xi)+R_(k)(jxi)” fora given jx, 5) using said α_(k)(jx) and corresponding jxi to define adata symbol estimate {circumflex over (Z)}_(k) for S_(k)(jx), 6) for k<Dcontinuing to fill memory M from the top down by replacing column xiwith column jx after moving the row elements of column xi down by onesymbol and placing {circumflex over (Z)}_(k) in the vacant first row,for all jx, 7) for k≧D continuing to replenish memory M from the topdown by replacing column xi with column jx after moving the row elementsof column xi down by one symbol and placing {circumflex over (Z)}_(k) inthe vacant first row, for all jx, 8) for k≧D selecting the last symbol{circumflex over (Z)}_(k−D) in column jx in the deleted bottom rowcorresponding to the maximium value of α_(k)(jx) over all jx, as thebest estimate of data symbol k−D, 9) for k>n continuing step 8 withoutreplenishing memory M to complete the estimates of the n data symbols,10) performing error correction decoding of these estimated datasymbols, wherein said QLM demodulated signal in a communicationsreceiver has been generated in a communications transmitter,up-converted to a radio frequency RF, power amplified, and transmittedas a RF QLM signal in a communications transmitter, and received in saidcommunications receiver, amplified, down-converted, and QLM demodulatedas described in this claim followed by decoding to recover the datasymbol information.
 5. The method in claim 4 for implementation of QLMdemodulation in a communications receiver for communications over thesame frequency bandwidth of a carrier frequency using time and/orfrequency and/or other offsets as the differentiating parameters andusing trellis symbol iterative demodulation, said method furthercomprising the steps: modifying said trellis symbol algorithm toiteratively include the correlation sidelobes by 1) implementing saidtrellis algorithm over the mainlobe correlation coefficients for thereceived correlated data symbols, 2) using data symbol estimates fromstep 1 to evaluate a contribution {circumflex over (X)}_(k|1) of thesidelobes enabling the hypothesized values {circumflex over(X)}_(k)(jxi) of received QLM correlated data symbols for all paths jxito be evaluated as the sum {circumflex over (X)}_(k)(jxi)={circumflexover (X)}_(k|0)(jxi)+{circumflex over (X)}_(k|1) wherein {circumflexover (X)}_(k|0)(jxi) is the hypothesized mainlobe contribution for alljxi, 3) repeating step 1 using a expression for {circumflex over(X)}_(k)(jxi), 4) continuing said iteration as required for convergenceto a stable solution, 5) completing the trellis algorithm with the errorcorrection decoding in said step 10, wherein said QLM demodulated signalin a communications receiver has been generated in a communicationstransmitter, up-converted to a radio frequency RF, power amplified, andtransmitted as a RF QLM signal in a communications transmitter, andreceived in said communications receiver, amplified, down-converted, andQLM demodulated as described in this claim followed by decoding torecover the data symbol information.
 6. The method in claim 4 forimplementation of QLM demodulation in a communications receiver forcommunications over the same frequency bandwidth of a carrier frequencyusing time and/or frequency and/or other offsets as the differentiatingparameters and using trellis bit demodulation, said method furthercomprising the steps: using said trellis symbol algorithm to implement atrellis bit algorithm by 1) implementing said trellis symbol algorithmwith data symbols reduced to a first bit b₀ for each of the receivedcorrelated data symbols in a first pass, 2) implementing errorcorrection decoding and re-encoding of the estimated first bits fromstep 1 to correct the decisioning errors if necessary, in the firstpass, 3) repeating step 1 using two-bit data symbol words b₀b₁ in asecond pass wherein bit b₀ is the estimate from the first pass and thesecond bit b₁ is estimated by the trellis algorithm, 4) for additionalbits in the data symbol words, repeat error correction decoding andre-encoding in step 2 for the second pass and implement step 3 in athird pass to estimate b₀b₁b₂ using the previous estimates of b₀b₁ fromthe second pass, 5) repeating step 3 for each additional bit in the datasymbol words, 6) continuing with these passes until the final bit passto estimate the data symbols, performing error correction decoding ofthese estimated data symbols, wherein said QLM demodulated signal in acommunications receiver has been generated in a communicationstransmitter, up-converted to a radio frequency RF, power amplified, andtransmitted as a RF QLM signal in a communications transmitter, andreceived in said communications receiver, amplified, down-converted, andQLM demodulated as described in this claim followed by decoding torecover the data symbol information.
 7. The method in claim 4 forimplementation of QLM demodulation in a communications receiver forcommunications over the same frequency bandwidth of a carrier frequencyusing time and/or frequency and/or other offsets as the differentiatingparameters and using trellis bit iterative demodulation, said methodfurther comprising the steps: using said trellis symbol algorithm toimplement said iterative trellis bit algorithm by 1) implementing atrellis symbol algorithm with the symbols reduced to the first bit b₀for each of the correlated data symbols in a first pass, 2) using bitestimates from step 1 to evaluate a contribution {circumflex over(X)}_(k|1) of the sidelobes enabling hypothesized values {circumflexover (X)}_(k)(jxi) of received QLM correlated data bits for all pathsjxi to be evaluated as a sum {circumflex over (X)}_(k)(jxi)={circumflexover (X)}_(k|0)(jxi)+{circumflex over (X)}_(k|1) wherein {circumflexover (X)}_(k|0)(jxi) is a hypothesized mainlobe contribution for alljxi, 3) repeating step 1 using this expression for {circumflex over(X)}_(k)(jxi), 4) continuing this iteration as required for convergenceto a stable solution, 5) implementing error correction decoding andre-encoding of the first bits to correct the decisioning error ifnecessary, 6) repeating steps 1-4 using two-bit data symbol words b₀b₁in a second pass wherein bit b₀ is estimated from the first pass and thesecond bit b₁ is estimated by the iterative trellis algorithm, 7) foradditional bits in the data symbol words, repeat error correctiondecoding and re-encoding in step 5 for the second pass and implementstep 6 in a third pass to estimate b₀b₁b₂ using the previous estimatesof b₀b₁ from the second pass, 8) repeating step 6 for each additionalbit in the data symbols, 9) continuing with these passes until the finalbit pass to estimate the data symbols, and 10) performing errorcorrection decoding of these estimated data symbols, wherein said QLMdemodulated signal in a communications receiver has been generated in acommunications transmitter, up-converted to a radio frequency RF, poweramplified, and transmitted as a RF QLM signal in a communicationstransmitter, and received in said communications receiver, amplified,down-converted, and QLM demodulated as described in this claim followedby decoding to recover the data symbol information.
 8. The method inclaim 4 or claim 5 or claim 6 or claim 7 for implementation of QLM in acommunications transmitter and a communications receiver forcommunications over the same frequency bandwidth of a carrier frequencyusing time and/or frequency and/or other offsets as the differentiatingparameters and using a demodulation method implemented with methods forreducing computational complexity, said methods for reducingcomputational complexity further comprising: reducing the number oftrellis states jx and transition paths jxi in the trellis algorithm byeliminating trellis states and trellis paths which have relatively poorvalues of the path metric α_(k)(jx) used to select a new data symbolestimate, reducing the number of trellis states by deleting lowercorrelation values of the sidelobes and mainlobe, modifying an iterativetrellis algorithm to calculate the forward trellis performance using theforward half of the mainlobe and followed by a backward trellisalgorithm using the other half of the mainlobe, modifying said iterativetrellis algorithm to incorporate said techniques to eliminate trellisstate and trellis paths with relatively poor performance metrics, usingsequential demodulation techniques, partial symbol and bit integrationover ΔT_(s) intervals and Δk intervals, and other demodulationtechniques as potential candidates for QLM demodulation, wherein saidQLM demodulated signal in a communications receiver has been generatedin a communications transmitter as disclosed in claims 1 and 2,up-converted to a radio frequency RF, power amplified, and transmittedas a RF QLM signal in a communications transmitter, and received in saidcommunications receiver, amplified, down-converted, and QLM demodulatedas described in this claim followed by decoding to recover the datasymbol information.